Cognitive arithmetic and problem solving: a comparison of children with specific and general mathematics difficulties

This study examined problem-solving and number-fact skills in two subgroups of third-grade children with mathematics difficulties (MD): MD-specific (n = 12) and MD-general (n = 12). The MD-specific group had difficulties in mathematics but not in reading, and the MD-general group had difficulties in reading as well as in mathematics. A comparison group of nonimpaired children (n = 24) also was included. The findings showed that on both story and number-fact problems, the MD-specific group performed worse than the nonimpaired group in timed conditions but not in untimed conditions. The MD-general group, on the other hand, performed worse than the nonimpaired group, regardless of whether tasks were timed or not. An analysis of children's strategies in untimed conditions showed that both the MD-specific and the MD-general groups relied more on backup strategies than the nonimpaired group. However, children in the MD-specific group executed backup strategies more skillfully than children in the MD-general group, allowing them to achieve parity with children in the nonimpaired group when tasks were not timed. The findings suggest that children with specific MD have circumscribed deficits associated with fact retrieval, whereas children with general MD have more basic delays associated with problem conceptualization and execution of calculation procedures.     

Cognitive sex differences and mathematics and science achievement.

Comments on the original article "Sex Differences in Intrinsic Aptitude for Mathematics and Science?: A Critical Review," by E. S. Spelke (see record 2005-15840-001). Spelke considered "three claims that cognitive sex differences account for the differential representation of men and women in high-level careers in mathematics and science." The focus of this comment is on the claim regarding gender differences in mean levels of cognitive abilities. Spelke claimed (p. 954) that "most investigators of sex differences have concluded that males and females have equal cognitive ability, with somewhat different profiles." There are two major components to this comment. The first is mainly theoretical, and the second is both theoretical and empirical. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teachers' knowledge of students' knowledge in mathematics problem solving: Correlational and case analyses.

This study examined the relationship of teachers' knowledge of students' knowledge to teachers' mathematics instruction and to students' mathematics problem solving. First-grade teachers (N?=?20) participated in a 4-week workshop in which they were given access to research-based knowledge on children's mathematics learning. Teachers were observed for 16 days throughout the school year. In May, teachers completed interviews and questionnaires about their knowledge and beliefs; their students completed achievement tests. Correlational analyses showed significant positive relationships between teachers' knowledge of students' knowledge and students' mathematics problem-solving achievement. Teachers with more knowledge of their students questioned students about problem-solving processes and listened to their responses. Teachers with less knowledge of their students explained problem-solving processes to students or observed students' solutions. Case analyses of knowledge and behavior of the most effective teacher and the least effective teacher supported these conclusions and showed important differences in how these teachers thought about and used students' knowledge. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Problem solving with equals: Peer collaboration as a context for learning mathematics and spatial concepts.

Assessed effects of peer collaboration on mathematical and spatial reasoning for fourth graders and on learning with logical-physical materials 1 year later. Subjects were 152 fourth graders, randomly divided into 4 groups: mathematics, spatial reasoning, and 2 control groups. In Year 1, pairs in the math and spatial groups worked together for six sessions on math and spatial problems, respectively. In Year 2, pairs of children in the math, spatial, and Control 1 groups worked together on a series of 6 sessions with balance scale problems. Findings from the pretest/posttest data indicated that peer collaboration is an effective learning environment for tasks that require reasoning, but not for tasks that require rote learning or copying. Furthermore, the learning that occurred in the second year was directly related to first-year gains made by pairs in the math group. Pretest gender differences in favor of boys diminished during the intervention. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Implicit learning in problem solving: The role of working memory capacity.

Participants solving the Balls and Boxes puzzle for the first time were slowed in proportion to the level of working memory (WM) reduction resulting from a concurrent secondary task. On a second and still challenging solution of the same puzzle, performance was greatly improved, and the same WM load did not impair problem-solving efficiency. Thus, the effect of WM capacity reduction was selective for the first solution of the puzzle, indicating that learning to solve the puzzle, a vital part of the first solution, is slowed by the secondary WM-loading task. Retrospective verbal reports, tests of specific puzzle knowledge, and a recognition test of potential strategies all indicated that participants were unaware of their knowledge of the puzzle, suggesting that it had been learned implicitly. Concurrent protocols collected from participants supported this conclusion and further suggested that participants were not aware of learning to solve the puzzle as this learning occurred. These results provide evidence that implicit learning depends on WM capacity and that implicit memory can play an important role in problem solving. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Federal policy for education in mathematics and science.

Suggests that the US is facing a national crisis in mathematics and science education, which is reflected in the shortage of qualified teachers at the elementary, secondary, and postsecondary levels. Salary incentives probably will be needed to increase the quality and quantity of science and math teachers. In addition to improving science and math education, there is a need to increase the public's understanding of the importance of science and technology. The passage of legislation (HR 1310) by the US House of Representatives is discussed, which defines the federal role in these areas and provides funding needed to address these problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive science and science education.

Discusses science education from a cognitive orientation that begins with the idea that to understand something, one must integrate it with already existing knowledge schemata. The paradox of science education is that its goal is to impart new schemata to replace the student's extant ideas that differ from the scientific theories being taught. Studies that illustrate the extent of the mismatch between the student's schemata and the expert's schemata are reviewed, and implications for instruction and for cognitive theories of learning are identified. Several characterizations of the differences between naive and scientific explanations are contrasted: the view from the cognitive science literature on the novice–expert shift, from the history of science on theory change, and from science educators and the works of Piaget. (39 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Enhancing third-grade student' mathematical problem solving with self-regulated learning strategies.

The authors assessed the contribution of self-regulated learning strategies (SRL), when combined with problem-solving transfer instruction (L. S. Fuchs et al., 2003), on 3rd-graders' mathematical problem solving. SRL incorporated goal setting and self-evaluation. Problem-solving transfer instruction taught problem-solution methods, the meaning of transfer, and 4 superficial-problem features that change a problem without altering its type or solution; it also prompted metacognitive awareness to transfer. The authors contrasted the effectiveness of transfer plus SRL to the transfer treatment alone and to teacher-designed instruction. Twenty-four 3rd-grade teachers, with 395 students, were assigned randomly to conditions. Treatments were conducted for 16 weeks. Students were pre- and posttested on problem-solving tests and responded to a posttreatment questionnaire tapping self-regulation processes. SRL positively affected performance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Problem solving and learning.

A. Newell and H. A. Simon (1972) provided a framework for understanding problem solving that can provide the needed bridge between learning and performance. Their analysis of means–ends problem solving can be viewed as a general characterization of the structure of human cognition. However, this framework needs to be elaborated with a strength concept to account for variability in problem solving behavior and improvement in problem-solving skill with practice. The ACT* theory (J. R. Anderson, 1983) is such an elaborated theory that can account for many of the results about the acquisition of problem-solving skills. Its central concept is the production rule, which plays an analogous role to the stimulus–response bond in earlier learning theories. The theory has provided a basis for constructing intelligent computer-based tutoring systems for the instruction of academic problem-solving skills. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conformity and problem solving.

Tests of problem solving, conformity, and intelligence were given to 77 women and 64 men introductory psychology students to investigate the possibility that conformity, a nonintellectual variable, contributes to the variability in achievement in problem solving. The results show a negative correlation between tendency to conform and achievement in problem solving when the influence of intelligence is statistically removed. 17 references. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Content effects in problem categorization and problem solving.

In many domains, the content of a problem (i.e., its surface cover story) provides useful clues as to the type of problem it is and to its solution. Five experiments examined this role of problem content on the problem solution and categorization of algebra word problems with experienced participants. In the first experiment, when problem content was atypical for the the problem's deep structure, people were worse at solving the problem. Differences were also detected in the problem solution where the problem's content was highly correlated with its deep structure versus problems where content was neutral to their deep structure. In the other experiments, problem categorization and determination of information relevance depended on how closely the problem's content matched its deep structure. These results suggest that content may be influential even for experienced problem solvers. The discussion examines the implications for problem schema access and application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions.

In 3 experiments, we examined the effects of using concrete and/or abstract visual problem representations during instruction on students' problem-solving practice, near transfer, problem representations, and learning perceptions. In Experiments 1 and 2, novice students learned about electrical circuit analysis with an instructional program that included worked-out and practice problems represented with abstract (Group A), concrete (Group C), or abstract and concrete diagrams (Group AC), whereby the cover stories were abstract in Group A and concrete in Groups C and AC. Experiment 3 added a 4th condition (C-A) with a concrete cover story and abstract diagrams. Group AC outperformed Groups A and C on problem-solving practice in Experiments 1 and 2 and outperformed Group C on transfer across the 3 experiments; Group AC also outperformed Group C-A in Experiment 3. Further, Group A outperformed Group C on transfer in Experiments 2 and 3 and outperformed Group C-A in Experiment 3. Transfer scores were positively associated with the quality of the diagrams and the number of abstract representations drawn during the transfer test. Data on students' learning perceptions suggest that the advantage of Group AC relies on the combined cognitive support of both representations. Our studies indicate that problem solving is fostered when learners experience concrete visual representations that connect to their prior knowledge and are enabled to use abstract visual representations. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Rapprochement among undergraduate psychology, science, mathematics, engineering, and technology education.

A discourse originating at liberal arts colleges has begun to influence national policy for science, mathematics, engineering, and technology education. The discovery-oriented, research-rich curriculum traditional for the graduate student is being developed for wider implementation in the service of new national goals. Though largely absent as a participant, the discipline of psychology has a great deal to contribute to and gain from joining in this agenda. The content of our field has many direct applications to the issues under consideration. We have common interests as a scientific field in developing science education. And, interdisciplinary and interinstitutional cooperation would be invigorating and constructive for our science, for our scholarship, and for our students. Psychologists should be proactive, not passive or reactive, in the improvement of undergraduate science education. This article presents both an invitation and an argument for fostering a new scientific and educational rapprochement. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Organization and creative problem solving.

"Groups from four populations differing in their amount of experience and identification with industrial vocation, were compared in their performances on the Change of Work Procedure problem." Arranged from most to least identified, there were 179 groups. "The results are interpreted as providing support for the proposition that the formal authority relations in organizations inhibit creative problem solving. They also suggest that business may be attracting people who can work comfortably, but not creatively, in such formal authority systems." (12 ref.) From Psyc Abstracts 36:04:4LI77M. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Sex differences in problem solving.

Used a 20-item set of problems (similar to those used by E. Sweeney [1953]) in 9 experiments with 558 male and 578 female undergraduates to determine which sex was superior in problem solving, the role of previous experience, whether sex differences extended throughout the domain of problem-solving tasks, whether they extended to other word problems, the role of spatial ability and verbal ability, the role of mathematics aptitude, and the relative importance of aptitude and social learning variables. Results show that the male advantage, averaging 35% across experiments, persisted at the same level as in experiments conducted in the 1950's. Sex differences extended to other word problems. The male advantage was related to similar advantages in spatial and mathematical ability. Aptitude variables dominated attitude and mathematics experience variables in accounting for the sex difference. (48 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Improving classroom learning by collaboratively observing human tutoring videos while problem solving.

Collaboratively observing tutoring is a promising method for observational learning (also referred to as vicarious learning). This method was tested in the Pittsburgh Science of Learning Center’s Physics LearnLab, where students were introduced to physics topics by observing videos while problem solving in Andes, a physics tutoring system. Students were randomly assigned to three groups: (a) pairs collaboratively observing videos of an expert human tutoring session, (b) pairs observing videos of expert problem solving, or (c) individuals observing expert problem solving. Immediate learning measures did not display group differences; however, long-term retention and transfer measures showed consistent differences favoring collaboratively observing tutoring. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Depression and social problem solving.

20 depressed patients with major depressive disorder, 20 nondepressed matched control Ss, and 17 patients with anxiety disorders were compared in different measures of social problem solving. Problem solving was assessed with the Means-Ends Problem-Solving Test (Study 1), the solution of personal problems, and a problem-solving questionnaire (Study 2). Results showed that, as predicted, depressed Ss suffered from a deficit in problem solving in all 3 measures. The majority of these deficits were also displayed by the clinical control group rather than being specific to a diagnosis of depression. However, depressed Ss produced less effective solutions than did normal and clinical control Ss. The results suggest that depressed and anxious patients may have difficulties at different stages of the problem-solving process. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Teaching thinking and problem solving: Research foundations.

Reviews 2 general research approaches to the development and effective teaching of reasoning, thinking, and problem solving. The first derives from studies of individuals who are experts in particular domains and emphasizes the role of domain-specific knowledge. The second emphasizes general strategic and metacognitive knowledge; ideally, people who develop the ability to learn new information and to monitor their current levels of proficiency will be able to function more effectively in a variety of contexts. Issues discussed include developmental and intraindividual differences, the representation of knowledge, means of facilitating memory access, and the concept of metacognition. It is concluded that many existing programs designed to teach thinking and problem solving could be strengthened by focusing more explicitly on domain knowledge, especially when students are helped to understand how different ways of learning new knowledge can affect their abilities to solve relevant problems. (3? p ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Metacognition and problem solving: A process-oriented approach.

Four studies were conducted to demonstrate that the positive effects of verbalization on solution transfer found in previous studies were not due to verbalization per se but to the metacognitive processing involved in the effort required to produce explanation for solution behaviors. In Experiments 1, 2, and 3, a distinction was made between process-oriented, problem-oriented, and simple "think aloud" verbalizations. The process-oriented (metacognitive) solvers performed significantly better than nonprocess control groups on both training and transfer tasks. Experiment 4 further demonstrated this effect by showing that process-oriented participants consistently form more sophisticated problem representations and develop more complex strategies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive science and military training.

Discusses how the massive scale and diversity of training needs in the military render it an enterprise that offers extensive opportunity for the application of cognitive science. Training in maintenance, in tactics, and in piloting or control of aircraft present several issues of interest to cognitive scientists. Four recently developed military training systems illustrate the potential for cognitive science to improve military training. These systems include a family of memorization games based on semantic networks; a simulator for steam propulsion plants with a graphic, schematic student interface; a system for training in problems of relative motion that provides explicit representations of spatial concepts and problem-solving procedures; and a method of building a new cognitive skill for air-intercept control based on principles for the development of automaticity. These systems illustrate the importance of making relevant knowledge concrete and explicit, of using problem-solving contexts for instruction in basic principles, and of careful management of information processing during learning. (28 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)